2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228421Counterexamples are presented to weighted forms of the Weiss conjecture in discrete and continuous time. In particular, for certain ranges of $α$, operators are constructed that satisfy a given resolvent estimate, but fail to be $α$-admissible. For $α\in (-1,0)$ the operators constructed are normal, while for $α\in (0,1)$ the operator is the unilateral shift on the Hardy space $H^2(\mathbb{D})$.16 pagesFunctional Analysis30C85, 30D50, 30H05, 47D06text